A South African Football Association (SAFA) envoy was in Rio de Janeiro this week and made him an official offer to succeed sacked compatriot Joel Santana, Parreira said on Thursday.
Brazil's 1994 World Cup-winning coach, who quit the South Africa job in April 2008 when his wife fell ill, said both sides were keen to seal his return by the end of the week.
He did not want to say whether he had accepted but made it clear in an interview with Reuters that his return was "on track".
"Some things still have to be approved, it's a decision that has to be made by the government," Parreira said.
"There's a proposal on the table that hasn't been signed but there is mutual interest.
"They have an urgent need because it's about the national team of the country that will host the World Cup... There has to be a solution by the end of the week."
The SAFA sacked Santana on Monday, less than eight months after he took charge on Parreira's recommendation, following a run of eight defeats.
He said he has been in regular contact with the Bafana Bafana's assistant coach Jairo Leal, who was with Parreira when he started the job in 2006 and stayed on under Santana.
"From the second round on it's a lottery. It will depend on the group which comes out of the draw. The hosts have greater expectations, their fans are emotional and rather irrational."
